The potential for the extraordinary island of Iceland to resolve seemingly intransigent problems in Earth Science has long been recognized. Alfred Wegener correctly surmised that his theory of continental drift could be tested there, and the necessary geodetic measurements were started as early as 1938. This, and other geophysical work often produced unexpected results. For example, observations reported before the acceptance of Wegener's hypothesis apparently supported it, while observations reported after its widespread acceptance seemed to contradict it. Iceland has always surprised us. In my presentation I shall report the most recent surprising findings. Long assumed to be one of very few places on Earth where sea-floor spreading can be observed on dry land, this model now requires modification. The convenience of studying oceanic crustal expansion on dry land apparently comes with a price. The crustal extension occurring in Iceland represents not classical seafloor spreading, with or without a mantle plume, but rather the process of continental volcanic margin formation–the process of continental breakup itself. I shall summarize the latest findings of an international group of collaborators of which I am privileged to be a member. I shall outline the rationale for our conclusion that Iceland, far from representing a simple oceanic spreading plate boundary on land, instead comprises magma-blanketed, extended continental crust. This theory is in need of evaluation through the collection of new, independent datasets that can test the predictions of the new model.